Percent of the original volume that is removed is; 18%
How to find the Volume of a box?
Formula for volume of a box is;
V = lbh
where;
l is length
b is breadth
h is height
Thus;
V_original = 15 * 10 * 8
V_original = 1200 cm³
Volume for each cube removed = 3 * 3 * 3 = 27 cm³
Since there are 8 corners on the box, then 8 cubes are removed.
So the total volume removed is; 8 * 27 = 216
Thus;
Percent of the original volume that is removed is;
216/1200 * 100% = 18%
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What is the exponent of 4 4?
In the expression 4^4, the number first 4 is called the base, and the next number 4 is called the exponent.
The exponent tells you how many times the base is being multiplied by itself. In this case, 4 is multiplied by itself 4 times.
4^4 = 4 x 4 x 4 x 4 = 256.So, the exponent of 4^4 is 4.
It's important to note that the exponent is also known as the power, so 4^4 is also read as 4 to the power of 4.
In summary, the exponent of 4^4 is 4. It tells you how many times the base (4) is being multiplied by itself. In this case, 4 is being multiplied by itself 4 times. Understanding this concept is important for solving mathematical problems, especially in algebra and calculus.
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What is the slope of y =- 5?
The slope of the given equation y = -5x is -5.
The equation y = -5x is a linear equation, which means that it is a function that can be represented in the form y = mx + b, where m is the slope and b is the y-intercept. The slope of a linear equation is the coefficient of x in the equation. In this case, the coefficient of x is -5, so the slope of the equation is -5.
It's worth noting that the slope represents the rate of change of the y-coordinate with respect to the x-coordinate, in other words, the steepness of the line. A slope of -5 means that for each unit increase in the x-coordinate, the y-coordinate will decrease by 5 units.
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The complete question is -
What is the slope of y = -5x?
How do I know if my cervix is dilating?
Knowing if your cervix is dilating typically involves a physical examination by a healthcare provider.
During labor, a healthcare provider will check the dilation of your cervix by performing a pelvic exam. They will use their fingers to feel the cervix, which is located at the top of the vagina, and determine the degree of dilation.
Cervical dilation is measured in centimeters, and full dilation is considered to be 10 centimeters. Before labor begins, the cervix is typically closed and has a firm consistency. As labor progresses, the cervix will start to soften and thin out, and will eventually open, or dilate.
Some women might experience Braxton Hicks contractions, which are sometimes referred as "false contractions" as they can be mistaken for the start of labor, but Braxton Hicks contractions do not cause cervical dilation.
It's important to note that dilation is just one of the factors that indicate that labor is imminent. It is not the only factor and some women can have a fully dilated cervix for days before going into active labor.
In conclusion, knowing if your cervix is dilating typically involves a physical examination by a healthcare provider, who will perform a pelvic exam to feel the cervix and determine the degree of dilation.
Cervical dilation is measured in centimeters, with full dilation being 10 centimeters. Be aware that dilation is just one of the factors that indicate labor is imminent.
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Rewrite g (x) = 3^-x when x = 7/5. Write this as an expression with a positive rational exponent and as an expression involving a radical. Show where g (7/5) would be located on the graph.
Step-by-step explanation:
g(x) = 3^-x
x = 7/5
so,
3^-(7/5)
the "-" says "1/...", therefore
1/(3^(7/5))
that is the expressing with the positive rational exponent.
with a fractional a/b exponent, "a" means "to the power of", and "b" means "pull the bth root".
so,
1/(3^(7/5)) =
[tex] \frac{1}{ \sqrt[5]{ {3}^{7} } } [/tex]
that is the expression with a radical.
to find the point find the origin (0, 0) point. from there go eighth on the x-axis to 7/5 = 1.4. and from there you go straight up to the curve. that is the point of g(7/5).
1/(3^(7/5)) = 0.214798005...
that is what the y value would be of that point.
by the way, the graph in the picture does not match the actual graph.
Please help me find value?
it would equal 2
sssssssssssssssssssss
i think it will equal to 2
Answer:
but im not sure
Using the constant of proportionality, write an equation for this proportional relationship:
You can buy 14 apples for 28 euros.
Use a to represent number of apples and c to represent the cost in euros. Please write your equation starting with c=
c = 14a/28
This equation represents the proportional relationship between the number of apples (a) and the cost in euros (c). The constant of proportionality is 14/28, which means that for every 14 apples, the cost is 28 euros. By dividing both sides by 14, we can also write the equation as a = c/2. This means that for every 2 euros, you can buy one apple.
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A population of field mice is 120. The population increas es at a rate of 9% a year. Write an exponential function that models
this situation:
Answer:
Population(year x) = 120*(1.09)^x
Step-by-step explanation:
Let x be the number of years from the time the population is 120 (year 0).
Population(year x) = 120*(1.09)^x
The 1.09 represents the growth for 1 year added to the initial population. E.g., year 1 would have a population of 120*(1.09)^1 or 140.8 (141). Year 2 would be 120*(1.09)^2 or 142.5 (143). And so on.
Each new year bilds on the prior year's ending population. In longhamd, this would be:
Year Pop.
0 120 120*(1.09)^0
1 141 120*(1.09)
2 120*(1.09)(1.09) or 120*(1.09)^2
3 120*(1.09)(1.09)(1.09) or 120*(1.09)^3
and so on.
the question is.
urine completed the square to solve the equation 0 = 3x to the square root of 2 - 9x + 27
Yes, Urie correctly completed the square to solve the equation 0 = 3x + 9 to the square root of 2 - 9x + 27.
How to solve square root equation? A square root equation is an equation that contains a square root of a variable, typically represented by the radical symbol √. To solve a square root equation, you must isolate the radical symbol on one side of the equation and then square both sides of the equation.For example, if the equation is √x + 3 = 7, you would need to subtract 3 from both sides to isolate the radical symbol on the left side of the equation. This would give you √x = 4. Then, square both sides of the equation to get rid of the radical symbol. This would give you x = 16, which is the solution to the equation.In general, to solve a square root equation, you must first isolate the radical symbol on one side of the equation. Then, square both sides of the equation to get rid of the radical symbol, which will give you the solution to the equation. It is important to remember to always square both sides of the equation, so that the equation is still balanced after the radical symbol is removed.To learn more about square root of equation refer to:
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The perimeter of a rectangle is 172 feet. Find the length and width if the length is an integer and the width is 2 times the next consecutive integer.
The length and width of the rectangle is 28 feet and 58 feet respectively.
How to find the sides of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
Therefore, the perimeter of a rectangle is the sum of the whole 4 sides of the rectangle.
Hence, the perimeter of a rectangle is 172 feet.
perimeter of a rectangle = 2(l + w)
where
l = lengthw = widthl = x
w = 2(x + 1) = 2x + 2
Therefore,
172 = 2(x + 2x + 2)
172 = 2(3x + 2)
divide both sides by 2
172 / 2 = 3x + 2
86 = 3x + 2
86 - 2 = 3x
3x = 84
divide both sides by 3
x = 84 / 3
x = 28
Therefore,
length = 28 feet
width = 2(28) + 2 = 58 feet
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find the rate of change of each function on the interval specified for real numbers
f(x)=x^2 +7 (4,w)
Answer:
w + 4
Step-by-step explanation:
The points (3, 9) and (–3, –9) are plotted on the coordinate plane using the equation y = a • x.
What is the value of a?
The value of {a} is equivalent to 3.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is the equation of a straight line → y = ax
The points (3, 9) and (–3, –9) are plotted on the coordinate plane using the equation y = ax, this means that -
9 = a x 3
a = 3
and
- 9 = a x - 3
a = 3
Therefore, the value of {a} is equivalent to 3.
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How do you find a quadratic function with a vertex and a point?
The quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero.
What is quadratic function?A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" shape. In mathematics, a quadratic issue is any problem that involves multiplying a variable by itself, often known as "squaring." This terminology comes from the fact that a square's area is equal to its side length multiplied by itself. The Latin term quadratum, which means square, is where the word "quadratic" derives.Three points are used to determine a quadratic function, which has the form f(x) = ax2 + bx + c. A quadratic function can be determined from three points on its graph by finding a, b, and c algebraically. Three equations and three unknowns must be solved in order to do this.
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How do you know when to change base?
When you are doing calculations, you can usually tell when you need to change base by looking at the problem. If the problem includes fractions, a base other than 10 may be more efficient. If the problem includes exponents, a base other than 10 may be necessary.
Changing Base for Complex CalculationsWhen working with numbers, it is important to know what base the numbers are in in order to correctly perform calculations. The base of a number is the number of digits used to express it, meaning that the base of a number can range from base 2 (binary) to base 36 (base 36 uses the numbers 0-9 and the letters A-Z).
Changing the base of a number can be helpful when dealing with fractions, exponents, and other complex calculations. To change the base of a number, divide the number by the base and then divide the remainder by the base, continuing to divide until the remainder equals 0.
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What type of dilation is formed when the scale factor K is greater than 1 blank options?
An expansion where image size increased is formed when scale factor k is greater than 1
What is Dilation ?The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.
The initial figure is referred to as the pre-image, and the new figure that results from dilatation is known as the image.
The resizing happens from a point called the center of dilation. It is the center of dilation from which the objects/figures are expanded or contracted. Scale factor is a number by which the size of any geometrical figure can be changed with respect to its original size.
when the scale factor K is greater than 1 , The image will enlarged
Hence, An expansion will be occur.
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i need help for part 2 it says Predict the population of the city in 30 years to the nearest whole number ( with steps please )
Predicting the population of the city in 30 years and to the nearest whole number with a decreasing population of 0.2% will give a value of
362,558How to predict the population in 30 yearsThe population is predicted by expressing the word problem as an exponential functions
An exponential function is a type of function that are of 3 main parts
the starting or initial valuebase function the exponentsConsidering the given problem, f(x) = 300(1.16)^x
the starting = 385 000
the base = 1 - r for decreasing where r is rate given as 0.2%
base = 1 - 0.2% = 0.998
the exponents = t
In the 30 years the population will be
= 385000 * (0.998)³⁰
= 362557.5623
= 362558
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What is the slope of the line described by the equation below
Answer: -3
Step-by-step explanation: Y=MX+B
Answer:
−3
Step-by-step explanation:
y-5=-3(x-17)
y=-3x+51+5
y=-3x+56
if we have this function:
y=mx+b
The slope is "m".
In this case, m=-3
Answer: sope -3
What are the zeros of quadratic function 2x² 7x 3?
The zeros of quadratic function 2x² - 7x + 3 = 0 are 3 and 1/2.
There are several methods for solving a quadratic equation of the form ax² + bx + c = 0. In our case, use the quadratic formula x = (-b ± √(b² - 4ac)) / 2a to find the zeros or the solutions for x.
Plug in the values to the formula and solve for x.
x = (-b ± √(b² - 4ac)) / 2a
x = (--7 ± √(-7² - 4(2)(3))) / 2(2)
x = (7 ± √49 - 24) / 4
x = (7 ± √25) / 4
x = (7 ± 5) / 4
x = 3 ; x = 1/2
Hence, the zeros of quadratic function 2x² - 7x + 3 = 0 are 3 and 1/2.
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NEED HELP ASAP - Algebra 2 - 50 Points
Do all logarithmic equations have a solution? Explain your reasoning and include an example.
What should we always check for when solving logarithmic equations?
Logarithmic equations with negative logs have no solution. Always use the original logarithmic equation to check for solved values.
What are the rules of Logarithms?The rules apply to any logarithm logbx, with the exception that any occurrence of e must be replaced with the new base b. Equations (1) and (2) defined the natural log. It is acceptable for x to be 0 or negative. However, when substituted or evaluated into the original logarithm equation, it is not allowed to have a logarithm of a negative number or a logarithm of zero, 0.
If we solve for x using log rules and properties, then plug those x values into the original equation, the equation should be satisfied. Also, keep in mind that the log's argument after plugging in the x values must be positive. There is no solution because the log's argument is negative.
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How do you construct a triangle class 7?
Building triangles entails using a protractor, a compass, and a ruler to build various triangles.
A triangle is a polygon with three sides. There are three angles, three vertices, and three sides to it. When the measurements are provided based on different qualities like SSS, SAS, and ASA, building triangles is simple.
These characteristics and guidelines must be understood in order to design a triangle:
(1) There are three sides presented (SSS – Side side side).
(2) Two sides are given, along with an angle (SAS – Side angle side).
(3) Two angles are shown, together with the included side (ASA – Angle side angle).
(4) The right triangle contains the measurements of the hypotenuse and a side (RHS – Right angle hypotenuse side).
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Identify the center of dilation.
-8
8
0
-4
ty
-8
8
Answer:The slope of the given line is -4
Step-by-step explanation:
27 5/3 in simplest radical form
The value of 27 5/3 in simplest radical form will be 86 / 3.
How to illustrate the exponent?The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Here the value of 27 5/3 in simplest radical form will be the calculated thus:
(27 × 3) + 5 / 3
= (81 + 5) / 3
= 86 / 3
The value in radical form will be 86 / 3.
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I need you to solve this
Answer:
Step-by-step explanation:
When dividing like bases (x is our base) we simplify by subtracting the exponents, top minus bottom. Since the exponents are fractions, we need a common denominator.
[tex]\frac{1}{5} -\frac{2}{15}=\frac{3}{15} -\frac{2}{15}=\frac{1}{15}[/tex]
thus, the simplification is [tex]x^\frac{1}{15}[/tex]
Answer:
(x 1/5)/(x 2/15)=.
(x1/5)× 15/2x
=15x/10x
=1.5
A pizza is cut into 10 equal slices. Eight friends each eat 1 slice. How much of the pizza did the friends eat? equation
Answer:
4/5
Step-by-step explanation:
What we know:
10 slices = 1 pizza8 friendsEach friend eats one slice1 slice = 1/10 of the entire pizza
8 friends * 1 slice / 10 slices =
8 * 1/10 = 8/10 of the pizza was eaten
8/10 = 4/5 of the pizza was eaten
7th grade math. .................................
Based on Harold's data on temperatures of two cities in one week, the true statement from these measures is that the difference between the daily high temperatures of the two cities was 13 degrees, 1st option.
What is a true statement?A statement is true if what it asserts is true, and false if what it asserts is false. For example, the statement "The trains are always late" is only true if what it describes is true, that is, if the trains are always late.
Also referred to as tautology. (Logic) a statement that must be true. truism. an obvious truth. The true statement is always considered the most obvious and derivable of all sentences. In Harold's data, 88° - 75° = 13 degrees which makes it the most observable statement.
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Maggie charges $15 an hour for babysitting on the weekend. She wants to make $105 this weekend so she can buy a new bag for school on Monday. She does not want to make more than $195 or she will have to pay tax on her earnings. What are the possible numbers of hours Maggie can babysit this weekend to make enough money for the bag she wants to buy without having to pay taxes on her earnings?
Answer:
7 - 13 hours
Step-by-step explanation:
This is just a common word problem.
Maggie gets charged $15 an hour and wants at least $105 and under $195
105 divided by 15 is 7 hours. 195 divided by 15 is 13 hours
The answer is she can babysit for 7 - 13 hours so she can make enough money for the bag she wants without having to pay taxes for her earnings.
Counting More Pebbles Along the Path page 1 of 2: Look at the pebbles along each part of the path. Fill in the missing numbers. 15 13 16 72 CHALLENGE Hansel and Gretel used a pebble to mark every 10 steps as they walked along the path. How many steps have they taken when they get to the last pebble on this part of the path? ____________Use numbers or words to explair how you know
The missing numbers are 14 and 17. there are 50 steps taken to reach the last pebble on this part of the path.
What is the missing number?
Missing numbers are the numbers that have been missed in the given series of a number with similar differences among them.
let's take a look at pebbles along each part of the path, there is 1 number of addition to each pebble number to go on next pebble.
i.e. 12, 13, 14, 15, 16, 17
so, the missing numbers are 14 and 17.
now, as given Hansel and Gretel used a pebble to mark every 10 steps as they walked along the path. How many steps have they taken when they get to the last pebble on this part of the path?
so, to go on next pebble there are 10 steps to walk.
therefore, from starting pebble number 12 to last pebble number 17, there are 50 steps ( difference between two pebbles is 10 steps).
hence, the missing numbers are 14 and 17. there are 50 steps taken to reach the last pebble on this part of the path.
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- 1 2/7x-1=26
Show work
The expression [tex]$1\frac{2}{7}x -1=26[/tex] gives {x} value as equivalent to 21.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the expression as -
[tex]$1\frac{2}{7}x -1=26[/tex]
We can write the expression as -
(9/7)x - 1 = 26
(9/7)x = 27
x = (27 x 7)/9
x = 3 x 7
x = 21
Therefore, the expression [tex]$1\frac{2}{7}x -1=26[/tex] gives {x} value as equivalent to 21.
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What is the solution to -6x - 7 = 35?
Answer:
Step-by-step explanation:
if it is 35 because if you put together two negative numbers they become positive
I hope it helps you :)
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Lets get it done ~[tex]\qquad \sf \dashrightarrow \: 6x - 7 = 35[/tex]
[tex]\qquad \sf \dashrightarrow \: 6x - 7 + 7 = 35 + 7[/tex]
[tex]\qquad \sf \dashrightarrow \: 6x = 35 + 7[/tex]
[tex]\qquad \sf \dashrightarrow \: 6x = 42[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 7[/tex]
One of the legs of a right triangle measures 7 cm and the other leg measures 17 cm. Find the measure of the hypotenuse. If necessary round to the nearest tenth.
Answer:
[tex]\huge\boxed{\sf H=18.4\ cm}[/tex]
Step-by-step explanation:
Given that,Base = 7 cm
Perpendicular = 17 cm
Hypotenuse = H
Using Pythagoras theorem.[tex](Hypotenuse)^2=(Base)^2+(Perpendicular)^2\\\\(H)^2=(7)^2+(17)^2\\\\(H)^2=49+289\\\\(H)^2=338\\\\Take \ square\ root \ on \ both\ sides\\\\\sqrt{(H)^2} =\sqrt{338} \\\\H=18.4\ cm\\\\\rule[225]{225}{2}[/tex]
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions.
PLEASE HURRY IM TAKING EXAM pre algebra
The equation which gives infinite solutions, x-10+x = 8+2x-18.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
For the infinite solution the both side of equation must contain equal quantity.
For example,
x-10+x = 8+2x-18
now, solving for x
x-10+x = 8+2x-18
2x-10 = 2x-10
-2x = -2x
-10 = -10
As, both sides are equal which shows the system of equation.
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